• Title, Summary, Keyword: 깁스 샘플링

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Bayesian Multiple Change-Point for Small Data (소량자료를 위한 베이지안 다중 변환점 모형)

  • Cheon, Soo-Young;Yu, Wenxing
    • Communications for Statistical Applications and Methods
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    • v.19 no.2
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    • pp.237-246
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    • 2012
  • Bayesian methods have been recently used to identify multiple change-points. However, the studies for small data are limited. This paper suggests the Bayesian noncentral t distribution change-point model for small data, and applies the Metropolis-Hastings-within-Gibbs Sampling algorithm to the proposed model. Numerical results of simulation and real data show the performance of the new model in terms of the quality of the resulting estimation of the numbers and positions of change-points for small data.

Bayesian Inference for Mixture Failure Model of Rayleigh and Erlang Pattern (RAYLEIGH와 ERLANG 추세를 가진 혼합 고장모형에 대한 베이지안 추론에 관한 연구)

  • 김희철;이승주
    • The Korean Journal of Applied Statistics
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    • v.13 no.2
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    • pp.505-514
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    • 2000
  • A Markov Chain Monte Carlo method with data augmentation is developed to compute the features of the posterior distribution. For each observed failure epoch, we introduced mixture failure model of Rayleigh and Erlang(2) pattern. This data augmentation approach facilitates specification of the transitional measure in the Markov Chain. Gibbs steps are proposed to perform the Bayesian inference of such models. For model determination, we explored sum of relative error criterion that selects the best model. A numerical example with simulated data set is given.

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Bayesian Inference for Littlewood-Verrall Reliability Model

  • Choi, Ki-Heon;Choi, Hae-Ja
    • Journal of the Korean Data and Information Science Society
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    • v.14 no.1
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    • pp.1-9
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    • 2003
  • In this paper we discuss Bayesian computation and model selection for Littlewood-Verrall model using Gibbs sampling. A numerical example with a simulated data is given.

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MCMC를 이용한 비동질적 포아송과정에서 일반화 순서통계량 모형의 연구

  • 최기헌;김희철
    • Communications for Statistical Applications and Methods
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    • v.4 no.3
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    • pp.753-763
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    • 1997
  • 컴퓨터의 발전에 따른 MCMC를 비동질적 포아송 과정에 이용하였다. 베이지안 추론에서 조건부 분포를 가지고 사후분포를 결정하는데 있어서의 계산 문제를 고려하였다. 특히 분포가 이중지수, 곰페르츠, 랄리, 감마, 그리고 검벨인 일반 순서통계량 모형에 대하여 깁스 샘플링과 메트로폴리스 알고리즘을 활용한 베이지안 계산과 모형선택을 제시하였다.

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Bayesian Approach for Software Reliability Models (소프트웨어 신뢰모형에 대한 베이지안 접근)

  • Choi, Ki-Heon
    • Journal of the Korean Data and Information Science Society
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    • v.10 no.1
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    • pp.119-133
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    • 1999
  • A Markov Chain Monte Carlo method is developed to compute the software reliability model. We consider computation problem for determining of posterior distibution in Bayseian inference. Metropolis algorithms along with Gibbs sampling are proposed to preform the Bayesian inference of the Mixed model with record value statistics. For model determiniation, we explored the prequential conditional predictive ordinate criterion that selects the best model with the largest posterior likelihood among models using all possible subsets of the component intensity functions. To relax the monotonic intensity function assumptions. A numerical example with simulated data set is given.

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Bayesian Inference for Modified Jelinski-Moranda Model by using Gibbs Sampling (깁스 샘플링을 이용한 변형된 Jelinski-Moranda 모형에 대한 베이지안 추론)

  • 최기헌;주정애
    • Journal of Applied Reliability
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    • v.1 no.2
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    • pp.183-192
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    • 2001
  • Jelinski-Moranda model and modified Jelinski-Moranda model in software reliability are studied and we consider maximum likelihood estimator and Bayes estimates of the number of faults and the fault-detection rate per fault. A gibbs sampling approach is employed to compute the Bayes estimates, future survival function is examined. Model selection based on prequential likelihood of the conditional predictive ordinates. A numerical example with simulated data set is given.

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Denoise of Synthetic and Earth Tidal Effect using Wavelet Transform (웨이브렛 변환을 응용한 합성자료 및 기조력 자료의 잡음 제거)

  • Im, Hyeong Rae;Jin, Hong Seong;Gwon, Byeong Du
    • Journal of the Korean Geophysical Society
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    • v.2 no.2
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    • pp.143-152
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    • 1999
  • We have studied a denoising technique involving wavelet transform for improving the quality of geophysical data during the preprocessing stage. To assess the effectiveness of this technique, we have made synthetic data contaminated by random noises and compared the results of denoising with those obtained by conventional low-pass filtering. The low-pass filtering of the sinusoidal signal having a sharp discontinuity between the first and last sample values shows apparent errors related to Gibbs' phenomena. For the case of bump signal, the low-pass filtering induces maximum errors on peak values by removing some high-frequency components of signal itself. The wavelet transform technique, however, denoises these signals with much less adverse effects owing to its pertinent properties on locality of wavelet and easy discrimination of noise and signal in the wavelet domain. The field data of gravity tide are denoised by using soft threshold, which shrinked all the wavelet coefficients toward the origin, and the G-factor is determined by comparing the denoised data and theoretical data.

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Bayesian Hierarchical Mixed Effects Analysis of Time Non-Homogeneous Markov Chains (계층적 베이지안 혼합 효과 모델을 사용한 비동차 마코프 체인의 분석)

  • Sung, Minje
    • The Korean Journal of Applied Statistics
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    • v.27 no.2
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    • pp.263-275
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    • 2014
  • The present study used a hierarchical Bayesian approach was used to develop a mixed effect model to describe the transitional behavior of subjects in time nonhomogeneous Markov chains. The posterior distributions of model parameters were not in analytically tractable forms; subsequently, a Gibbs sampling method was used to draw samples from full conditional posterior distributions. The proposed model was implemented with real data.

The Bayesian Analysis for Software Reliability Models Based on NHPP (비동질적 포아송과정을 사용한 소프트웨어 신뢰 성장모형에 대한 베이지안 신뢰성 분석에 관한 연구)

  • Lee, Sang-Sik;Kim, Hee-Cheul;Kim, Yong-Jae
    • The KIPS Transactions:PartD
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    • v.10D no.5
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    • pp.805-812
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    • 2003
  • This paper presents a stochastic model for the software failure phenomenon based on a nonhomogeneous Poisson process (NHPP) and performs Bayesian inference using prior information. The failure process is analyzed to develop a suitable mean value function for the NHPP; expressions are given for several performance measure. The parametric inferences of the model using Logarithmic Poisson model, Crow model and Rayleigh model is discussed. Bayesian computation and model selection using the sum of squared errors. The numerical results of this models are applied to real software failure data. Tools of parameter inference was used method of Gibbs sampling and Metropolis algorithm. The numerical example by T1 data (Musa) was illustrated.

Bayesian Change Point Analysis for a Sequence of Normal Observations: Application to the Winter Average Temperature in Seoul (정규확률변수 관측치열에 대한 베이지안 변화점 분석 : 서울지역 겨울철 평균기온 자료에의 적용)

  • 김경숙;손영숙
    • The Korean Journal of Applied Statistics
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    • v.17 no.2
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    • pp.281-301
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    • 2004
  • In this paper we consider the change point problem in a sequence of univariate normal observations. We want to know whether there is any change point or not. In case a change point exists, we will identify its change type. Namely, it can be a mean change, a variance change, or both the mean and variance change. The intrinsic Bayes factors of Berger and Pericchi (1996, 1998) are used to find the type of optimal change model. The Gibbs sampling including the Metropolis-Hastings algorithm is used to estimate all the parameters in the change model. These methods are checked via simulation and applied to the winter average temperature data in Seoul.